期刊
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
卷 15, 期 2, 页码 471-479出版社
SPRINGER BASEL AG
DOI: 10.1007/s12346-015-0179-3
关键词
Averaging method; Melnikov function; Limit cycle bifurcation
资金
- National Natural Science Foundation of China [1271261, 11431008]
- Slovenian Research Agency
- NNSF of China [11271252]
- RFDP of Higher Education of China [20110073110054]
- innovation program of Shanghai Municipal Education Commission [15ZZ012]
- European Community Framework Programme [FP7-PEOPLE-2012-IRSES-316338]
There is a folklore about the equivalence between the Melnikov method and the averaging method for studying the number of limit cycles, which are bifurcated from the period annulus of planar analytic differential systems. But there is not a published proof. In this short paper, we prove that for any positive integer k, the kth Melnikov function and the kth averaging function, modulo both Melnikov and averaging functions of order less than k, produce the same number of limit cycles of planar analytic (or C-infinity) near-Hamiltonian systems.
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